Group Signatures with Message-Dependent Opening: Formal Definitions and Constructions

Box 5

The Abe-Haralambiev-Ohkubo signature scheme, where denotes the message length (in group elements) of the scheme. The algorithm randomizes a pair under the constraint that the pairing is unchanged. The algorithm produces a set of pairs and which are uniformly random with the constraint that .

SigKg:

 ,

 For :

,

 ,

 Output

Sign:

 , , ,

 Output

Verify:

 If

 and then

Output

 Else

Output

Rand:

 If and then

Output

 Else

If then

Output

Else

If then

Output

Else

Output

Extend:

Output